Ref.: Ms. No.
GERG-D-07-00084
COSMOLOGICAL IMPLICATIONS OF CLASSICAL KALUZA
RELATIVITY
General Relativity and Gravitation
Dear Dr
williams,
Reviewers' comments on your work have now been
received. You will see that they are advising against publication of
your work. Therefore I must reject it.
For your guidance, I
append the reviewers' comments below.
Thank you for giving us
the opportunity to consider your work.
Yours sincerely
George
Ellis, Ph.D.
Editor-in-Chief
General Relativity and
Gravitation
Reviewers' comments:
Reviewer #1: This
paper resurrects Kaluza's original theory without
attempting to
address any of the arguments against that theory, which
have long
since led to its abandonment. I do not recommend it for
publication
in General Relativity and Gravitation.
Briefly:
1) the
cylinder condition is imposed "by fiat"; no explanation is
given why the extra coordinate is to be treated differently from
the
others. Such a procedure may have been acceptable in 1921,
but it
was already out of date by 1926 when Klein provided the
first physical
explanation for cylindricity (namely
compactification). The author
of the present paper offers no such
explanation, instead justifying
the assumption of the cylinder
condition as a "minimal form of the
theory which reproduces
standard 4D theory." This is not a scientific
approach.
2)
even if some mechanism such as compactification is supposed, a
paper
reviving Kaluza's theory must address another of the historical
reasons for its abandonment; namely, the hierarchy problem. When
one
follows Klein's approach, leading to a hierarchy of
"Kaluza-Klein
modes" for every particle, it is natural
to hope that the same
hierarchy would account for the
quantization of electric charges, as
well as masses of elementary
particles. However, the charge-to-mass
ratios of the n=1 modes
turn out to be all wrong for describing,
e.g., electrons and
protons (as Klein had originally hoped). The
practice later on
was instead to associate observed particles with
n=0 modes. These
are, however, massless at the level of the field
equations, and
one has to go through additional steps to endow them
with mass,
so that the whole theory becomes a great deal more
complicated
(and, to some perhaps, more artificial).
3) the author seems
confused about scalar fields, the third great
reason why Kaluza's
idea never caught on historically. In some
places, he seems to
want to set the scalar equal to a constant, which
is of course
necessary if one wants to get Maxwell electromagnetism
out of
Kaluza's theory in 4D. But a scalar field that is everywhere
constant is no scalar at all, and completely artificial from a
modern
point of view. (It was occasionally considered in the
context of
certain problems, e.g. by Bergmann in his book [Ref.
6], but he
introduced "special coordinate systems" for
this purpose, obviously
not a covariant approach.)In other
places, the author wants to let
the scalar field vary with time.
Then one no longer gets
electromagnetism from the Kaluza
mechanism. The author proceeds
nonetheless, and finds that the
gravitational "constant" G evolves
like t squared. Such
a variation would be in gross disagreement with
observational
bounds from, e.g., the Mars Viking lander experiments.
I do
not see any way to remedy this paper so as to make it suitable
for
publication in GRG. Generations of physicists have wrestled with
Kaluza's beautiful idea in the hope of building a unified theory
of
fundamental interactions. Those who would push this work
further
must first understand what has gone before.
Reviewer
#2:
The author revises the classical Kaluza-Klein theory arguing
that
the fifth diagonal element of the metric, a scalar field, is
constant
on non-cosmological scales. This, it is claimed, is a
natural
consequence of the theory and does not need to be imposed
a priori.
The author then studies the cosmological implications
of the theory:
-The gravitational constant is directly related
to a universal
charge to mass ratio, eq.(16);
-The
gravitational constant relates the 5th dimensional coupling of
the
electromagnetic field to gravity;
-The electric charge arises from
motion along the 5th dimension and
it is not a conserved
quantity, eq.(19);
-The scale factor of the universe can vary
proportionally to cosmic
time during the radiation dominated
epoch.
I worry, however, whether the theory can provide a
viable
cosmological scenario. Surely if the scale factor varies
proportionally to the cosmic time during radiation domination,
the
rate of expansion must be significantly different from the
standard
one at the time of nucleosynthesis which can potentially
be dangerous
for the nucleosynthesis predictions of the light
elements abundances.